Kontsevich–Soibelman [1]} defined a Cohomological Hall algebra of \((Q,W)\)  inspired by the Donaldson-Thomas theory of the Jacobi algebra \(\text{Jac}\,(Q,W)\) :
\(\text{CoHA}\,(Q, W):=\bigoplus _{d\in \mathbb {N}^I}H^{\cdot }\left(\mathcal {X}(d), \varphi _{\text{Tr}\,W}\mathbb {Q}\right),\) 
